Super-exponential tracking for nonlinear systems with non-vanishing uncertainties

In this paper we introduce a general and systematic approach to achieving robust tracking control for nonlinear systems with non-vanishing uncertainties, along with the complete rejection of non-vanishing uncertainties and user-assignable convergence rate. Furthermore, the convergence rate can be pre-specified faster than exponential or nearly as fast as any prescribed finite time if needed. The key design tool is the utilization of a time-varying feedback gain through a time-varying scaling function that satisfies certain conditions. A general way to construct such time-varying rate function is given such that the different yet assignable convergence rates can be achieved.